### Abstract

The distribution of the surplus immediately prior to ruin in the classical compound Poisson risk model was considered in a paper by Dufresne and Gerber (1988). The main purpose of this paper is to present a simple method for finding the distribution function and the density function of this surplus. We show that explicit solutions for these functions can be found when we know the probability and severity of ruin, denoted G(u, y). We also derive an algorithm which can be used to give approximate values of the distribution function when explicit solutions cannot be found. We also briefly consider the joint density of the surplus immediately prior to ruin and the deficit at the time of ruin. © 1992.

Original language | English |
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Pages (from-to) | 191-207 |

Number of pages | 17 |

Journal | Insurance: Mathematics and Economics |

Volume | 11 |

Issue number | 3 |

Publication status | Published - Oct 1992 |

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### Keywords

- Probability of ruin
- Recursive calculation
- Severity of ruin
- Surplus prior to ruin

### Cite this

*Insurance: Mathematics and Economics*,

*11*(3), 191-207.

}

*Insurance: Mathematics and Economics*, vol. 11, no. 3, pp. 191-207.

**On the distribution of the surplus prior to ruin.** / Dickson, D. C M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the distribution of the surplus prior to ruin

AU - Dickson, D. C M

PY - 1992/10

Y1 - 1992/10

N2 - The distribution of the surplus immediately prior to ruin in the classical compound Poisson risk model was considered in a paper by Dufresne and Gerber (1988). The main purpose of this paper is to present a simple method for finding the distribution function and the density function of this surplus. We show that explicit solutions for these functions can be found when we know the probability and severity of ruin, denoted G(u, y). We also derive an algorithm which can be used to give approximate values of the distribution function when explicit solutions cannot be found. We also briefly consider the joint density of the surplus immediately prior to ruin and the deficit at the time of ruin. © 1992.

AB - The distribution of the surplus immediately prior to ruin in the classical compound Poisson risk model was considered in a paper by Dufresne and Gerber (1988). The main purpose of this paper is to present a simple method for finding the distribution function and the density function of this surplus. We show that explicit solutions for these functions can be found when we know the probability and severity of ruin, denoted G(u, y). We also derive an algorithm which can be used to give approximate values of the distribution function when explicit solutions cannot be found. We also briefly consider the joint density of the surplus immediately prior to ruin and the deficit at the time of ruin. © 1992.

KW - Probability of ruin

KW - Recursive calculation

KW - Severity of ruin

KW - Surplus prior to ruin

UR - http://www.scopus.com/inward/record.url?scp=38249009745&partnerID=8YFLogxK

M3 - Article

VL - 11

SP - 191

EP - 207

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

IS - 3

ER -